Advertisements
Advertisements
प्रश्न
Integrate the function:
`sqrt(1+ x^2/9)`
Advertisements
उत्तर
Let `I = int sqrt (1 + x^2/9) dx`
`= 1/3 int sqrt (9 + x^2) dx`
`= 1/3 int sqrt (x^2 + 3^2) dx`
`= 1/3 [x/2 sqrt (x^2 + 9) + 9/2 log |x + sqrt (x^2 + 9)|] + C`
`...[∵ int sqrt (a^2 + x^2) dx = x/2 sqrt (a^2 + x^2) + a^2/2 log |x + sqrt (a^2 + x^2)| + C]`
`= x/6 sqrt (x^2 + 9) + 3/2 log |x + sqrt (x^2 + 9)| + C`
APPEARS IN
संबंधित प्रश्न
find : `int(3x+1)sqrt(4-3x-2x^2)dx`
Integrate the function `1/sqrt(1+4x^2)`
Integrate the function `1/sqrt((2-x)^2 + 1)`
Integrate the function `(3x)/(1+ 2x^4)`
Integrate the function `1/sqrt(x^2 +2x + 2)`
Integrate the function `1/sqrt(7 - 6x - x^2)`
Integrate the function `1/sqrt(8+3x - x^2)`
Integrate the function `(4x+ 1)/sqrt(2x^2 + x - 3)`
Integrate the function `(x + 2)/sqrt(x^2 -1)`
Integrate the function `(6x + 7)/sqrt((x - 5)(x - 4))`
Integrate the function `(x + 2)/sqrt(4x - x^2)`
Integrate the function:
`sqrt(1- 4x^2)`
Integrate the function:
`sqrt(x^2 + 4x + 6)`
Integrate the function:
`sqrt(1-4x - x^2)`
`int sqrt(x^2 - 8x + 7) dx` is equal to ______.
Find `int dx/(5 - 8x - x^2)`
Integration of \[\frac{1}{1 + \left( \log_e x \right)^2}\] with respect to loge x is
\[\int\frac{1 + x + x^2}{x^2 \left( 1 + x \right)} \text{ dx}\]
Find : \[\int\left( 2x + 5 \right)\sqrt{10 - 4x - 3 x^2}dx\] .
Find `int (dx)/sqrt(4x - x^2)`
Evaluate \[\int \frac{dx}{a^2-x^2}\].
Evaluate \[\int \frac{dx}{x^2+a^2}\].
Evaluate \[\int \frac{dx}{\sqrt{x^2+a^2}}\].
Which factorization is used before applying partial fractions to \[\frac{1}{x^2-a^2}\]?
Which trigonometric substitution is suitable for \[x^2+a^2\] and \[\sqrt{x^2+a^2}\]?
Which expression is the general transformation obtained by completing the square?
What is \[\frac{d}{dx}(ax^2+bx+c)\]?
Evaluate \[\int\frac{dx}{3x^2+13x-10}\].
Which statement is correct when integrating an expression that is not immediately a standard integral?
